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Sapors for heat engines 

INCLUDING 

CONSIDERATIONS RELATING TO THE USE OF 
FLUIDS OTHER THAN STEAM FOR POWER 
GENERATION: A STUDY OF DESIRABLE VAC- 
UUM LIMITS IN SIMPLE CONDENSING EN- 
GINES: METHODS FOR COMPUTING EFFI- 
CIENCIES OF VAPOR CYCLES WITH LIMITED 
EXPANSION AND SUPERHEAT: A VOLUME- 
TEMPERATURE EQUATION FOR DRY STEAM: 
AND NEW TEMPERATURE-ENTROPY DIA- 
GRAMS FOR VARIOUS ENGINEERING VAPORS 



BY 

WILLIAM DUANE ENNIS, M.E., Mem. Am. Soc. M.E. 

Professor of Mechanical Engineering in the Polytechnic Institute of Brooklyn 
Author of "Applied Thermodynamics for Engineers," etc. 



WITH 21 TABLES AND 17 ILLUSTRATIONS 




NEW YORK 

D. VAN NOSTRAND COMPANY 

23 MURRAY AND 27 WARREN STREETS 
1912 



• 



A 



Copyright, 1912, 

BY 

D. VAN NOSTRAND COMPANY 



/£.-%{/ 



THE SCIENTIFIC PRESS 

ROBERT DRUMMOND AND COMPANY 

BROOKLYN, N Y. 



CCU312197 



LIST OF ILLUSTRATIONS 



FIG. PAGE 

1. The Clausius Vapor Cycle 4 

2. Pressure-Temperature Relations of Engineering Vapors 9 

3. The Binary Vapor Principle 26 

3'. Turbine Characteristics 29 

4. Comparative Proportions of Power Plants, Complete Expan- 

sion Cycle 32 

5. Rankine Cycle for Dry Vapor 35 

(5. Effect of Change in Back Pressure 40 

7. Comparative Proportions of Power Plants, Rankine Cycle ... 56 

8. Rankine Cycle with Superheat 59 

9. Temperature- Volume Curves for Dry Steam 73 

10. Temperature-entropy Chart for Alcohol 44 

11. Temperature-entropy Chart for Chloroform 46 

12. Temperature-entropy Chart for Acetone 48 

13. Temperature-entropy Chart for Carbon Chloride and Carbon 

Bisulphide 51 

11. ( 1 yclic Efficiencies and Criterion 53 

If). Temperature-entropy Diagram for Ether 37 

16. Temperature-entropy Diagram for Ammonia 71 

17. Temperature-entropy Diagram for Carbon Dioxide 74 

v 



VAPORS FOR HEAT ENGINES 



i 



General Considerations as to the Choice of a Working 

Fluid 

Water is the working substance in the great majority 
of external-combustion heat engines. It so far surpasses 
all other vapors in cheapness that it alone can be considered 
for use in a non-condensing cylinder. With condensing 
operation, the fluid may be mostly saved, to be used over 
and over again in a closed cycle; and if the loss by leakage 
is not too great, some other vapor may replace steam. 

To get a rough idea of the amount of leakage permissible, 
suppose a pound of coal, containing 14,000 B.T.U., to 
generate steam at 70 per cent efficiency, so that 

14,000X0.70 = 9800 B.T.U., 

are contained in the steam. Let this heat perform work 
in a steam engine at 10 per cent efficiency, 

9800X0.10 = 980 B.T.U., 

being converted into useful work per pound of coal burned. 
Suppose also that some other fluid were i 1 ,, more efficient 



2 VAPORS FOR HEAT ENGINES 

than steam, i.e., that it could drive a heat engine at 11 
per cent efficiency. In obtaining 980 B.T.U. of useful 
work we should then consume 

9804-0.11 =8909 B.T.U. 

of heat in the vapor of the assumed fluid. If this fluid 
could be generated at the same boiler efficiency as steam, 
the heat necessary in the coal would be 

8909^-0.70 = 12,727 B.T.U., 

a saving of 14,000-12,727 = 1273 B.T.U. or 9.1 per cent, 
in fuel cost, which might offset the expense due to leakage 
of fluid in operation. 

Suppose this new fluid to cost, pound for pound, the same 
as coal: leakage amounting to 9.1 per cent would be per- 
missible; if it costs twice as much as coal, the alloAvable 
limit of leakage would be 4.55 per cent; if it costs ten times 
as much as coal, the leakage limit is tVo of one per cent, 
and so on. There are volatile vapors which might be used in 
heat engines, costing not more than ten times as much 
as coal; and there are vapors permitting, under certain con- 
ditions, of an efficiency exceeding by T V that attainable 
with steam. With a leakage loss below 1 per cent, an 
investigation of the possibilities in applying these vapors to 
power production should be not without interest. 

Engines have actually been built using ether, sulphur 
dioxide, gasoline, alcohol and ammonia, among other vapors 
besides steam. Ammonia, not steam, is the fluid commonly 
used in the cylinders of refrigerating compressors; steam 
would of course not answer; but the expense due to leakage 
of ammonia is not ordinarily a matter of vital importance. 



II 

Data for the Analysis 

In what follows, it will be assumed that the Carnot 
formula, 

V- {A) 

is recognized as an expression in terms of the absolute 
temperatures for the ideal limiting efficiency of any heat 
engine whatever, working between the temperatures specified. 
For a vapor engine, however, there is an equally definite 
and lower limit of efficiency. Some acquaintance with the 
temperature-entropy diagram must now be assumed. In 
Fig. 1, ordinates are absolute temperatures, abscissas are 
entropies, horizontal lines are isothermals (and also, for 
saturated vapors, lines of constant pressure), vertical lines 
are acliabatics. The area under any line, down to the ON 
axis, represents the heat absorbed or emitted in working 
the substance along the corresponding path. The ideal 
cycle for a vapor initially dry is abed, ab being the path of 
constant pressure and nearly constant specific heat followed 
in heating the liquid, be the path of vaporization, cd that of 
adiabatic expansion, and da that of condensation at con- 
stant pressure. The cycle Ibcd is that of Carnot, bounded 
by isothermals and adiabatics alone. It is an impracticable 
cycle for a vapor. 

3 



4 VAPORS FOR HEAT ENGINES 

The efficiency of the cycle abed is, 



Heat converted into work 



abed 



Gross amount of heat expended eahef 

_ eabk + kb cf—eadf 
eabk-\-kbcf 



■ (B) 



32 °F. 





Fig. 1. — The Clausius Vapor Cycl< 



If the upper and low r absolute temperature limits of the 
cycle be T and t respectively, L and I being the corresponding 
heats of vaporization, then I 

. L I 

bc = y, aq = -; 

-t 
and if the specific heat of the liquid be constant and equal to c, I 



7 fdH CedT f T dT . T 

al= J T=J~T~ = c J i T- =clogc T' 



the H and T in the first integral denoting heat and temper- 
ature; respectively, in general- If h and h a denote the 



DATA FOR THE ANALYSIS 5 

respective heats of the liquid corresponding with the absolute 
temperatures T and t, we have as a definite expression for 
the efficiency l of the cycle abed, 

ho — ha+L 1 

aq 

. h b -ha+L ' 

C log e y+y, 
= 1 ~*' h-ha+L (C) 

Eq. (C) is, however, inapplicable for the purpose in 
hand, because c is in general quite variable. We may use 
successive values of c for computing changes of entropy for 
short temperature ranges and thus obtain a close approx- 
imation to the change for any finite range. 

The values of c over the short temperature ranges chosen 
in the exemplifying table on. page 6, are, of course, obtained 
by dividing the differences of " heats of liquid " by those 

T 

temperature ranges. The expression — denotes the quotient 

t 

of absolute temperatures expressing the range. 

If now we sum up the figures in the last column, we shall 

have a series of figures representing the entropies of liquid 

(abscissas of the path yb in Fig. 1) at various temperatures, 

these entropies being tabulated above 32° F. as an arbitrary 

1 This statement of efficiency has been preferred by the writer, 
although some authorities compute efficiencies on the basis of heat 
absorbed above 32°, making the denominator in Eq. (C) simply H c 
(total heat in dry steam) = the area oybcf, Fig. 1. But even in bad 
practice water is fed to the boiler at a higher temperature than 32°; 
so that it seems reasonable, in establishing ideal standards, to assume 
it to be delivered thereto at the temperature at which it is rejected by 
the engine. 



VAPORS FOR HEAT ENGINES 



Table I 
COMPUTATION OF ENTROPY OF LIQUID OF ALCOHOL 





Heal 
of the 
Liquid 


Differences, 


Corre- 
sponding 

Value 
of c 




T 

t 




Tempera- 
ture, ° F. 


Tempera- 
ture 


Heat of 
Liquid 


clo SeJ 


32 





— 


— 


— 




— 


— 


50 


10.06 


18 


10.06 


0.559 


510 

492 


= 1.036 


0.0198 


08 


20.56 


18 


10.50 


. 583 


528 
510 


= 1.035 


0.0204 


86 


31.48 


18 


10.92 


0.607 


546 

528 


= 1.033 


0.0198 


104 


42.68 


18 


11.20 


0.622 


564 
546 


= 1.032 


0.0200 


122 


54.38 


18 


11.70 


0.650 


582 
564 


= 1.031 


0.0206 


140 


67.27 


18 


12.89 


0.716 


600 

582 


= 1.031 


0.0227 


158 


80 . 24 


18 


12.97 


0.721 


618 
600 


= 1.030 


0.0214 


176 


93.80 


18 


13.56 


. 753 


636 
618 


= 1.029 


0.0211 


194 


107.95 


18 


14.15 


0.786 


654 
636 


= 1.028 


0.0217 


212 


122.72 


18 


14.77 


0.821 


672 
654 


= 1.027 


0.0223 


230 


138 . 13 


18 


15.41 


0.856 


690 
672 


= 1.027 


0.0232 


248 


154.21 


18 


16.08 


0.894 


708 
690 


= 1.026 


0.0230 


266 


170.96 


18 


16.75 


0.931 


726 
708 


= 1.025 


0.0225 


284 


188.46 


18 


17.50 


0.972 


744 

726 


= 1.024 


0.0230 


302 


206.68 


18 


18.22 


1.012 


762 
744 


= 1.023 


0.0235 



DATA FOB THE ANALYSIS 7 

starting point. The distance al on the diagram may then 
be written, 

al = yz—yx = n b — n a , 

where n b and n a denote, respectively, these tabulated entro- 
pies of the liquid for the two points specified. The symbol 
n tc will be employed for entropy of liquid in general, measured 
a 1 ove32 F. 

Again, widths like be, from the liquid to the saturation 
curve, are always equal to the quotient of latent heat of 
vaporization by absolute temperature; that is, to 

L I 

T or T 

These quantities may also be tabulated for various tem- 
peratures, the general symbol being n e ; or, referring to Fig. 
1, ribc, n aQ , etc. Finally, by adding the values of n w and n e , 
for any temperature, we have that of n s , the total entropy 
of the dry vapor at the same temperature. 

These three properties 1 have been tabulated for all of 
the vapors to be considered (except steam) in Table XXI. 

We may now write Eq. (B) in the form, 

■nrc • h b —ha-\-L — t(n b — n a +n hc ) n 

Efficiency = J^+Z • • (O 

which is the exact expression for the cycle with complete 
adiabatic expansion. 

1 The vapor properties employed in this discussion have been taken 
from the appendices to Vol. II of Zeuner's Technical Thermodynamics, 
Klein Edition (D. Van Nostrand Co.). The tables of entropies were, 
however, compiled by the writer from data given by Zeuner, especially 
for the present work. 



» VAPORS FOR HEAT ENGINES 

The Pressure-temperature Relation. This must be 
clearly understood: that a fluid boils at a definite tempera- 
ture for every pressure to which it may be subjected; the 
greater the pressure, the higher is this temperature; a vapor 
cannot exist, as such, at a temperature below that which 
thus " corresponds " with its pressure; but, by superheating, 
it may be brought to any higher temperature desired. The 
lower the pressure at which a non-superheated vapor is 
formed, the greater is the space which it occupies; and 
(an important fact in the subsequent discussion) this even 
holds in a rough, approximate way for vapors generally, so 
that if for any boiling-point we should tabulate the cor- 
responding pressures of a number of vapors, and afterward 
the spaces occupied by unit weight (the specific volumes) 
of the same vapors, we should find that they ranked, in 
order of pressures, somewhat inversely as they ranked in 
order of specific volumes. 

In Fig. 2, we have plotted the pressure-temperature 
curves of various vapors from the figures given in Table II. 
The curve for steam occupies the extreme right-hand posi- 
tion; i.e., its pressure, at a given temperature, is less than 
that of any other vapor considered. 






DATA KOI! TIIK ANALYSIS 



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n . 






- c 5 = * s ffp^f— * 




■F- — H+T H 



-20 20 40 60 '80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380400 
TEMPERATURE IN FAHRENHEIT DEGREES 



Fig. 2. — Pressure-Temperature Relations of Engineering Vapors 



Ill 

The Limit of Efficiency with Steam 

The maximum pressure at which steam is commonly 
worked on a commercial scale is 250 lbs., corresponding 
to a temperature of, very nearly, 400° F. With superheat, 
temperatures up to 600°, or even higher, are employed. 
These limits of temperature may be easily accounted for 
on mechanical and commercial grounds. They are not 
necessarily permanent. 

There are equally definite (and far more permanent) 
limits of lower temperature. A vapor cannot exist at a 
temperature lower than that corresponding with its pres- 
sure. If an engine exhausts into the atmosphere, the tem- 
perature of heat rejection cannot be less than that cor- 
responding with a pressure of 14.696 lbs. per square inch — 
212° F. If it exhausts into a vacuum of 28 inches of mer- 
cury, the corresponding temperature is 100° F. Lower 
than these temperatures we cannot go. The best average 
vacuum that can be commercially maintained is not over 
28 ins. The pressure of steam is then only 0.946 lb. per 
square inch. It has been brought to its condition of greatest 
attenuation outside the laboratory. By applying Eq. (A), 
taking the Fahrenheit zero as 460° above the zero absolute, 

10 



THE LIMIT OF EFFICIENCY WITH STEAM 11 






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12 VAPORS FOR HEAT ENGINES 

we have the following as the ideal limits of efficiency in 
steam engines according to present practice: 

Non-condensing, saturated steam, — =0.22; 

Condensing, saturated steam, inruudRin = ^' 35, 

^ , . i_ 600-100 n „_ 

Condensing, superheated steam, fin h-Mfif) = 0,47 - 

The best actual (cylinder) thermal efficiency ever recorded 
for a vapor engine was about 0.25. 



IV 

The Line of Attack 

Suppose we assume a pressure of 250 lbs. or a tem- 
perature of 600° (with superheat) to determine the upper 
limit of the cycle, and a vacuum of 28 inches to fix the lower 
limit. The use of a vapor other than steam might then, 
apparently, be justified on one of three grounds: 

1. A higher temperature might be attained at 250 lbs. 
pressure, without superheat. 

2. A temperature of 600° might be attained by super- 
heating, with an efficiency higher than is possible from 
steam at that temperature. 

3. A lower temperature might be attained at 28 ins. 
of vacuum. 

If, as in Fig. 2, we plot curves with temperatures as 
abscissas and corresponding pressures as ordinates, con- 
ditions 1 and 3 taken together require a vapor giving a 
curve which crosses that for steam. At a very low pressure, 
we wish the boiling-point to be lower than that of steam; 
and at higher pressures, its boiling-point should be the 
greater. No such vapor is known to the writer. It is not 
impossible that one may exist, for similar crossings of the 
pressure-temperature curves occur with other pairs of fluids. 
For example, the carbon chloride and ethyl alcohol curves, 
in Fig. 2, show a crossing point near 190° F.; our hypothetical 
vapor should give a curve related to that of steam in much 

13 



14 VAPORS FOR HEAT ENGINES 

the same way as the carbon chloride curve is related to that 
of alcohol. Its properties would have to be somewhat as 
indicated by the dotted line. 

Condition 1 is easy to meet. There are many known 
vapors giving curves lying wholly to the right of the steam 
curve in Fig. 2; but these vapors have the general dis- 
advantage of giving a higher temperature than steam at 28 
ins. of vacuum, so that condition 3 is violated. 

Condition 3 would lead to a lower temperature of heat- 
rejection, and thus increase the potential efficiency of the 
cycle; but in any case this temperature cannot be below 
that of the average available supply of cooling water; or, 
say, in our latitude, about 60° F. The limit of efficiency 
with superheat, for any vapor, would then be, from Eq. (A), 

60 °- C0 0.51, 



600+460 



an increase of about 8 per cent over the present limit with 
steam. 

If we disregard the possible existence of such a vapor as 
is designated by the dotted line of Fig. 2, and for the present 
restrict the discussion to saturated (non-superheated) 
vapors, we must obviously dwell upon Condition 3. The 
vapor to be preferred is one which boils at about 60° F. 
(any lower temperature is needless, on account of the cool- 
ing water limit, and likely to lead to excessive maximum 
pressures) at an absolute pressure of from 1 to 4 lbs. per 
square inch. Carbon bisulphide, chloroform, acetone and 
carbon chloride (with possibly alcohol) are the only fluids 
to be considered (see Appendix I) . The last (carbon chloride) 
requires the best vacuum — a moderate one, however — but 
is most desirable from the standpoint of maximum pressure, 
as indicated on page 15. 



THE LINE OF ATTACK 15 

Table III 
MAXIMUM PRESSURES WITH VARIOUS VAPORS 

Vapor Pressure in^bs.^per Sq.in., 

Alcohol 142 

Chloroform 140 

Acetone 163* 

Carbon bisulphide 176 

Carbon chloride 88 

Steam 69 

* Extrapolated. 

The pressure with carbon chloride is only 28 per cent 
greater than that with steam. The indication is that at 
higher temperatures the excess percentage will be less, the 
two curves in Fig. 2 perhaps crossing near 400° F., our 
assumed upper limit with saturated steam. It may then be 
that the " suggested ideal vapor " of Fig. 2 really exists, 
as carbon chloride, the curve for which resembles the dotted 
curve shown, excepting that it occupies a position further 
toward the left. In such case, the objection to the use 
of carton chloride as a substitute for steam ? with an accom- 
panying 8 per cent increase in potential efficiency, is the 
probable expense due to leakage. 



Efficiencies of Dry Vapors in the Complete Expansion 
Cycle 

Considering now the diagram abed of Fig. 1, to which 
Eqs. (B), (C) and (Z>) apply, we may examine the efficiencies 
shown by these equations as representing more nearly the 
limits of practice. It is first proposed to establish a criterion 
for estimating relative efficiencies in advance. 

The cycle abed is less efficient than the Carnot cycle 
ahed drawn through the same extreme limits. The work 
areas are: Carnot, ahed: Clausius 1 i abed; and the amounts 
of heat chargeable are; Carnot, ehef; Clausius, eabef. The 
excess of heat chargeable in the case of the Carnot cycle 

1 It is a current, but (the writer believes) unjustifiable, habit to 
refer to the complete expansion cycle abed, Fig. 1, as Rankine's. It 
does not appear that Rankine ever described such a cycle, although 
Clausius did, in his Fifth Memoir on the Application of the Mechanical 
Theory of Heat to the Steam Engine. Rankine shows the adiabatic 
expansion cycle with terminal drop (incomplete expansion) in The 
Steam Engine, 1897 Ed., Art. 278; and this is the cycle which should 
properly be associated with his name. The Clausius (complete expan- 
sion) cycle is perfectly definite for a given dry vapor. The temperature 
limits fully determine the efficiency, just as in the Carnot cycle. It 
is the ideal cycle of a vapor engine. The terminal drop Cycle, on the 
other hand, is indefinite and establishes no standard for comparison 
with results obtained in actual engines. Any number of such cycles, 
of various degrees of efficiency, is possible between two given temper- 
ature limits. 

16 



COMPLETE EXPANSION CYCLE 17 

is ahb; but the excess of work obtained is also ahb, so that 
this work is obtained at 100 per cent efficiency. Whatever 
makes the Clausius cycle more nearly like that of Carnot 
increases the efficiency of the former. The ideal work 
area should be rectangular, not trapezoidal. Departure of 
the area abed from rectangular form is due wholly to the 
slope of the line ab. This slope varies with the specific 
heat of the liquid, since the entropy or abscissa of the path 

ab, {at), has been shown to be equal to c log e —, where c is 

la 

that specific heat. When c = 0, ab is vertical and abed is 
a rectangle. 

Further, slope of the line ab becomes less important 
in producing deviation of the area abed from rectangular 
form when the width be is relatively great. This width 

is — , the quotient of the latent heat of vaporization by the 

absolute temperature. At any temperature, then, it is 
desirable that the latent heat should have a high value. 
Considering both factors, the most efficient fluid is likely 
to be that for which there is obtained at a given temperature, 
the maximum value of 

L _ Latent heat of vaporization 
c Specific heat of the liquid 

The following table applies this (not new) principle to Fig. 1. 



18 



VAPOKS FOR HEAT ENGINES 



> O 



° *» 


















*■« T 1 














o ^ 


cc 


Tj- 


CC 


<M 


to 


rH 














^_^ 














.1. <a 


e'- 


CC 


C 


<M 


lO 


.o 


er: 


CC 


t^ 


lO 


t^ 




^ a, 


Tfl 


Tt 


CC 


to 


CO 


o^ 
















,-^ 














ii § 


tc 


3 


cc 


1> 


o 


o 


o 


c 


CC 


1— 1 


CO 


r- 


J] ~ 


O 


tO C\ 


co 


d 


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00 


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r-i 




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I 



COMPLETE EXPANSION CYCLE 19 

Steam appears likely to give the most efficient cycle, 
carbon chloride nearly the least efficient. If we now apply 
Eq. (D), taking additional values from the entropy tables, 
page 78, we obtain: 

Definitive Vapor Efficiencies 
Alcohol, 

186.12+306.86-52 8(0.325 0-0.0402+0.40 3) 

492.98 ' 

Chloroform, 

56.37+92.94-528(0.1077-0.0172+0.1219) _ 

149.31 -U.^4J; 

Acetone, 

134.24*+178.11*-528(0.2465*-0.0368+0.236*) 

312.35 • '" ' 

Carbon bisulphide, 

58.29+117.90-528(0.1099-0.0172+0.154) 

176.19 -0.250; 

Carbon chloride, 

49.93+69.02 - 528(0.0953 - 0.0145+0.0905) 

118.95 -0.238; 

Steam, 

235.53+908.00-528(0.4398-0.0707+1.1921) 
1143.53 



= 0.279: 



the order of efficiencies being substantially as predicted. 
The efficiency of the Carnot cycle between the same tem- 
perature limits is 

302-68 .... 

302+460 = a30b - 

* Extrapolated. 



20 VAPORS FOR HEAT ENGINES 

But while four of the six vapors could in practice be 
worked down to a temperature of 68° F. without difficulty, 
this would be impossible with steam or with alcohol. Steam, 
for example, would at this temperature exert a pressure of 
only 0.34 lb. per square inch, equivalent to a vacuum of 
29.2 ins. With a more practicable lower temperature limit 
— say 110° F. — the efficiency of the Clausius cycle, using 
steam, would be (from Eq. (D)) only 

271.60-77.94+908.00-570(0.4398-0.1471 + 1.1921) 

271.60-77.94+908.00 ' 

slightly lower than that obtainable with the better temper- 
ature range possible with the other vapors. A reduction 
in lower temperature limit is thus shown likely to be prof- 
itable (though only slightly so) when the matter is viewed 
under conditions more closely corresponding to practice 
than those of the Carnot cycle. 

It appears, then, that an engine using the vapors of 
chloroform, acetone, carbon bisulphide or carbon chloride 
would, with a less perfect vacuum than is now common in 
steam plants, permit of an efficiency somewhat exceeding 
that attainable with steam. Expansion is assumed to be 
complete, and (in some cases at least) the maximum pressure 
would be increased. 



VI 

Superheat 

This conclusion is unsatisfactory in that some excess 
of initial pressure is involved. It is true that with carbon 
chloride the excess is not great, and might at the upper 
limit of 400° become nil; but with this vapor the gain 
in efficiency is also small and might disappear if 400° F. 
were fixed as the upper temperature. 

We might avoid excessive pressures by superheating, 
while at the same time increasing efficiency; but steam can 
be superheated as well as the other vapors. We have 
assumed that it is virtually a pressure condition, rather 
than a temperature condition, which establishes the lower 
limit of our cycle; the vacuum necessary must not exceed 
about 28 ins. of mercury. Let us now accept a pressure 
condition as also establishing the upper limit and examine 
a superheated cycle in which a maximum ten>jierature of 
600° is attained at a pressure not exceeding 100 lbs. per 
square inch. 

Is there in this case any criterion from which we may 
hazard an advance guess, as with the saturated vapor cycles, 
regarding the probable order of efficiencies? The area abcig, 
Fig. 1, represents the operation to be considered. Com- 
paring it with the former cycle abed, we find the added* 
work area, dcig, to consist of the two parts dejg and cij. 
The increased expenditure of heat may similarly be divided 
into the two parts ; fcjm, giving the work area dejg (a Carnot 

21 



22 VAPORS FOR HEAT ENGINES 

cycle), and cij, giving a work area equivalent to itself. The 
first work area is necessarily obtained at slightly greater 
efficiency than the original Clausius cycle abed between 
the same temperature limits. The latter work area is equal 
to the heat which it costs. It is gained at 100 per cent 
efficiency, and is the potent factor in making the cycle 
abcig more efficient than abed. 

The extent to which superheating will increase cyclic 
efficiency is thus c'osely related to the ratio of the areas 
cy, abed. The former area will be large when T~T C is large 
and when the width cj is large. The former condition is 
approached as T c decreases, for Ti has been fixed at 600° F. 
We have also established the pressure at c as 100 lbs. We 
wish, then, for a vapor in which the saturation temperature 
at 100 lbs. pressure is relatively low; that is, a vapor lying 
to the left of the steam curve in Fig. 2. 

Again, the width cj is directly proportional to the specific 
heat of the superheated vapor. The slope of the constant 
pressure path of superheat, ci, is related to this constant, 
just as the slope of the liquid line, ab, is related to the specific 
heat of the liquid. Considering both conditions, then, 
the most desirable vapor will be that in which 

(a) The specific heat during superheating is large, and 

(6) The temperature at 100 lbs. pressure is small. 

Superheated steam has, undoubtedly, the highest specific 
heat of any of the vapors under discussion. That of alcohol 
(0.4534) approaches it, while that of chloroform, for example, 
is only 0.1567. Whether the better pressure-temperature 
relations of these two vapors may offset their less desirable 
specific heat values can be determined only by computing 
the efficiencies in detail. The advance criterion of efficiency 
is in this type of cycle indefinite; but we may at least pre- 
sume that alcohol will give a more favorable result than 
chloroform, on account of its much higher specific heat. 



SUPERHEAT 



23 



We will then examine the cycle in which 7 7 i = 600° F., 
the maximum pressure is 100 lbs., and the lower pressure 
is not less than 1 lb. For steam, at 1 lb. absolute pressure, 
the lower temperature limit will be 101.83°; for alcohol, 
it will be 72°; while for chloroform, since it would be only 
28°, we will regard the cooling water as establishing a lower 
limit at 60° F. The following thermal properties are tabular: 

Table V 
" VAPOR PROPERTIES FOR CYCLES WITH SUPERHEAT 



Vapor. 


Tc 


h 


ta 


fl n 


Lie 


Tic 


k* 


n n 


Steam .... 
Alcohol . . . 
Chloroform 


327.8 
277.0 
270.3 


298.3 

181.8 
57.0 


101.83 
72.00 
60.00 


69.8 
23.0 
6.54 


888.0 
320.0 
96.37 


1.602 
0.728 
0.229 


0.52 

0.4534 

0.1567 


0.1327 
0.0446 
0.0134 



* Specific heat of the superheated vapor. 

The expression for efficiency is, if the expansion line 
crosses the saturation curve, 



abcig abke + kbcf+fcim — agme 



eabcim 



abke + kbcf+fcim 
= 1 



(ni—n a )t a 



h-ha+Ltc+klTt-Tc) 



. . (E) 



Where n is the symbol for entropy above 32° F. In order 
to find rii, we write, 



T 

n ( -n c = &log e ^, 



(F) 



ric being tabular and T t always 600+460 = 1060. Then, 
For steam, n t = 1.602+ (o.52x2.3 log ~^\ =1.7558; 



24 VAPORS FOR HEAT ENGINES 

For alcohol, n, = 0.728+ ^0.4534X2.3 log I^q) =0.8925; 

and 

For chloroform, w,= 0.229+ ^0.1567X2.3 log ^\) = 0.2874. 

But in the general case the vapor may remain superheated 
at the end of expansion, giving such a cycle as pbcino, Fig. 1. 
To determine whether this is the case for our conditions, 
we have only to compare values of nt and n 0f the latter being 
the total entropy of the dry vapor at the lower temperature, 
and having the following values: for steam, 1.9754; for 
alcohol, 0.857; and for chloroform, 0.2416. Since n 
exceeds nt for steam, the cycle is like abcig, and Eq. (E) 
is applicable, yielding, 

„ , , (1.7558-0.1327)561.83 

Forsteam > 1 -228.5+888.0+0.52(272.2) = °' 272 ' 

But for alcohol and chloroform another equation must be 
found, applicable to such a cycle as pbcino. This equation is 

pbcino 



Efficiency = 



h-hp+LK+HTt-Tc) 



1 _ J^po\K{l n 1 ) , ~x 

h h -h p -\-L ic +k{T t -T c y ' ' w 
in which T n is to be found from the relation 

T 

n i —n P =n vo +n on = n vo +k\og e -~ l - . . . (H) 

1 o 

The values of L p0 are respectively 433.01 and 117.91; those 
of n p0 are 0.814 and 0.2278. Applying Eq. (H), 



T„ = 571° absolute or 111° F .; 



For alcohol, 0.8925-0.0446 = 0.814+1 
and 



SUPERHEAT 25 

while for chloroform, 

0.2874-0.0134 = 0.2278+ (o.1567X2.3 log ^Y 

\ 520/ 

and 

T» = 706° absolute or 246° F. 

The corresponding efficiencies, from Eq. (G), are 

1 433.01+0.4534(111-72) Q7C ... 

*~ 478.8+ (0.4534X323) =°' 278 f ° r alcoho1 ' 



and 



- 117.91+0.1567(246-60) n oro , ,. . 
1 - 146.83 + (0.1567X329.7) = °- 259 f ° r chloroform > 



confirming the prediction made, in spite of the greater tem- 
perature range with chloroform. Alcohol and steam are 
about equally efficient, while chloroform is decidedly less 
desirable under these superheated conditions. The values 
of k taken are somewhat uncertain, and this property is 
too variable to warrant our drawing any closer conclusions; 
but it seeems safe to say that there is no inherent advantage 
on the part of either of the proposed vapors in a complete 
expansion condensing engine using superheated steam; 
the three efficiencies seem to have no relation to the con- 
denser temperature. We cannot by superheating, con- 
sequently, evade the high initial pressures to which excep- 
tion has been taken, without at the same time losing the 
efficiency advantage shown under certain circumstances to 
be possible. 



VII 



The Binary Vapor Principle 

High initial pressure may, however, be eliminated by the 
vapor engine of Du Tremblay, in which steam, discharged 
from a cylinder at, say 110° F., may be condensed by the 





Fig. 3. — The Binary Vapor Principle 
abcd= primary tfgh= binary Ideally, idcj = khefl 



circulation of a more volatile fluid in the condenser coils. 
This second fluid is thus vaporized and may be used to 
perform work in a second cylinder. We may thereby 
work down to the cooling water limit of temperature — 
about 60° F. — and so obtain the slight increase in efficiency 
that our calculations have shown to be possible, without 
any increase in maximum pressure. Commercially, this 

26 



THE BINARY VAPOE PRINCIPLE 27 

gain is insufficient to offset the added complications. The 
principle has been applied, intermittently, in actual engines 
for at least sixty years, with the expected economical 
thermal result, if not with commercial success. Fig. 3 shows 
the combined ideal indicator and entropy diagrams. The 
initial and back pressures on the two cylinders will usually 
differ, though not always in the way here indicated. There 
might be a mechanical advantage in having them equal. 



VIII 



Application to the Turbine 

The Clausius cycle analyzed is that of the steam turbine 
rather than that of the reciprocating engine; in -which latter, 
cylinder condensation makes anything like complete expan- 
sion undesirable. The nozzle velocities obtained from a 
frictionless adiabatic flow, adopting the usual approximate 
formula, V = 224:Vh, where H is the cyclic area in B.T.U., 
may be computed as follows : these cyclic areas are the numer- 
ators of the efficiency expressions given in sections V and VI, 
so that if the efficiencies be each multiplied by their respective 
denominators we have at once the required numerators. 



Table VI 
CYCLIC AREAS AND NOZZLE VELOCITIES 
Vapor E_ V 

(a) 302° to 68°, Vapors Initially Dry 

Alcohol 0.264X 492.98 = 130.0 2550 

Chloroform 0.249X 149.31= 37.1 1360 

Acetone 0.246X 312.35= 77.0 1960 

Carbon bisulphide . . 0.260X 176.19= 45.9 1520 

Carbon chloride . 238 X 1 18 . 95 = 28 . 3 1 190 

Steam 0.279X1143.53 = 319.0 4000 

(b) Initially Dry Vapor, 302° to 110° 
Steam... 0.231X1101.66= 255.0 3570 

(c) Vapors with Superheat at 600° F. 

Steam 0.272X1257.5 =342 4150 

Alcohol 0.278X 625.0 =174 2960 

Chloroform 0.259X 198.48= 51.3 1600 

28 



APPLICATION TO THE TURBINE 



29 



The variation in velocities is notable. These velocities 
are of course proportional to the square roots of the quan- 




Fig. 3'. — Turbine Characteristics with Frictionless Buckets 

(a) (6) 

Jet velocity ab, ab' ab 

Peripheral velocity ac, ed ac, ac', ed, e'd' 

Absolute exit velocity ec, e'c e'c', ec 

Rotative components of ] . .. . ... , ,.. , . 

absolute exit velocities} cf > cf (negatlve) <*''/' (negative) 

tities of heat converted into work in the various cycles con- 
sidered; and in the actual working out of a turbine design, 
the question of absolute emerging velocity is fundamentally 
related both to mechanical limitations and to the obtained 



30 VAPORS FOR HEAT ENGINES 

efficiency. Our efficiency equations have been applicable 
to ideal conditions only. The velocity of flow will be an 
important factor in determining how nearly the actual 
turbine will approach the ideal efficiency. 

To consider this subject in all of its bearings would 
require a somewhat extended discussion. We may briefly 
point out three facts: 

(1) With a given nozzle angl and peripheral speed, 
and with buckets of usua form a relative y low nozzle 
velocity is apt to lead to a retarding reaction at exit. (See 
Fig. 3', a.) 

(2) With a given nozzle angle and nozz'e velocity, 
positive exit reactions are associated with the lower periph- 
eral speeds. (See Fig. 3', b). 

(3) With a given nozzle ang e the per pheral speeds of 
impulse turbines using various vapors will with usual 
bucket angles vary about as the nozzle velocities of those 
vapors. 

An efficient velocity turbine would therefore be possible 
at low peripheral speeds, with these special vapors, without 
excessive compounding into pressure stages. 



IX 
Some Commercial Considerations 

Boiler Capacity. The argument is sometimes advanced, 
in connection with a'cohol vapor launch engines, that the 
low value of the latent heat of vaporization of this fluid 
is an advantage in that less time and less boiler surface are 
required to " get up steam." 

The size or capacity of a steam boiler is measured by 
its heating surface. Under the conditions which normally 
exist a heat transmission of about 33,000 B.T.U., per square 
foot of surface per hour, is considered reasonable. Very 
nearly the same conditions hold, regardless of the particular 
fluid contained in the boiler. With boilers of a given type, 
the quantity (volume) of fluid contained will bear a fairly 
constant ratio to the heating surface and therefore to the 
heat transmission. 

In a power p ant, the efficiency of the engine determines 
the quantity of heat to be supplied by the vapor leaving 
the boiler, per horse-power-hour. This efficiency, therefore, 
determines also the heating surface of the boiler, and, 
from the conc'usion already reached, it determines the 
volume of liquid in the boiler. 

The " time to get up steam " for a given volume of 
liquid in the boiler will depend also upon the specific volume 
of that liquid. Finally, therefore, boiler capacities neces- 
sary with various fluids may be expected to vary inversely 
as the cyclic efficiencies; the times consumed in starting 

31 



32 



VAPORS FOR HEAT ENGINES 



up the boilers will vary inversely as the products of efficiency 
by specific volume of liquid. The data for comparison are 
given in Table VII, volumes being taken at 212° F. The 
" quick steaming " boiler will, however, lack steadiness, 
and the comparison really means very little, for quickness 



100 




98 




i 
89 




93 




94 




88 



Steam 



Carbon 
Chloride 



Carbon Chloroform Acetone 
lisulphide 

Relative Boiler Capacities Necessary 



Alcohol 




Steam 



Carbon 
Chloride 



Carbon 
Bisulphid* 



Chloroform Acetone Alcohol 



Relativ 


b Times Rec 


nil 


•ed to "C 


jet Up Steam ' 


' in a Given 


Boiler 


102 




99 




88 




93 




95 




87 



Steam 



Chloroform Acetone 



Alcohol 



Carbon Carbon 

Chloride Bisulphide 

Relative Amounts of Condenser Surface and Cooling Water 



Fig. 4. — Comparative Proportions of Power Plants Using Various 
Fluids in the Complete Expansion Cycle, All Initially Dry Vapors 
and All Developing the Same Horse-power 

of steaming might be attained in any case by using a type 
of boiler having a low ratio of liquid contents to heating 
surface. 

Cooling Water. In Fig. 1, the area abed represents work 
done and the area eadf represents heat which must be removed 
by the condenser. The ratio of the latter area to the for- 



SOME COMMERCIAL CONSIDERATIONS 



33 



Table VII 
BOILER CAPACITY AND STEAMING RATE 
Clausius Cycles with Vapor Initially Dry 



Vapor 


Efficiency 


Relative 
Boiler 

Capacity 


Volume 

of 
Liquid 


Volume 

X 
Efficiency 


Relative 

Time to 
"Get up 

Steam " 


Alcohol 

Chloroform 

Acetone ,••••• 

Carbon bisulphide. . . 

Carbon chloride 

Steam 


0.204 
0.249 
0.246 
. 2G0 
0.238 
0.231 


88 
93 
94 
89 
98 
100 


0,0208 

0.009G 
0.0192 
0.0130 
0.0069 
0.0160 


0.00549 
. 00238 
. 00472 
0.00339 
0.00104 
0.00370 


68 
15G 

78 
109 
225 
100 



Temperature limits: for steam, 302° and 110°; for the other vapors, 
302° and 08°. 



mer therefore varies directly as the cooling water consump- 
tion per horse-power, and as the amount of condenser sur- 
face necessary. The values of this ratio show no great 
variation; what difference exists is unfavorable to steam. 
The following is the comparison for the conditions adopted 
in Table VII: 

Table VIII 

CONDENSER SURFACE AND COOLING WATER 
CONSUMPTION 



Vapor. 



Area, 
abed 



Area, 

cadf 



Alcohol 130.0 

Chloroform 37.1 

Acetone 77.0 

Carbon bisulphide. . . . 45.9 

Carbon chloride ...... 28 . 3 

Steam 255.0 



362.98 
112.21 
235.35 
130.29 
90.65 
846.66 



cadf 


■r-abed 


2 


80 


3 


02 


3 


06 


2 


84 


3 


20 


3 


31 



Relative Condenser 

Surface and Coolinf.' 

Water Consumption 

per Horse-power 



87 
93 
95 
88 
99 
102 



These commercial factors are represented graphically in 



Fig. -1. 



X 

The Rankine Cycle 

This is shown in Fig. 5. Expansion terminates before 
the pressure has been reduced to that of the exhaust, and 
the pressure falls at constant volume (line rs in both diagrams) 
at the outer end of the stroke. The heat converted into 
work is abcrs: the gross amount of heat expended is, as in 
the Clausius cycle, eabcf=h b — h a -{-Lc. The efficiency of 
the former cycle is obviously less than that of the latter. 

The area of this cycle may be regarded as the algebraic 
sum of the quantities of external work done along the three 
paths be, cr and sa, which quantities may be denoted by the 
symbol W with appropriate subscripts. Now Wb C = PV Cl 
Wsa = pV s ; and by the common formula for adiabatic 
expansion, 

Wcr = h+r c — hu — Xrr h ....(/) 

in which expressions V denotes the vapor volume at the 
subscript state and r the " internal latent heat of vaporiza- 
tion." Then 

abcrs = PV c — pV s -\-hi,-{-rc—hu—Xrrt. . . (J) 

The conditions of the problem give all quantities except- 
ing x r , n and V s . If we assume a limiting temperature 
at r, these also may be readily computed, for n is tabular 
for a given value of t r , and 

X T li 



h 



34 



THE RANKINE CYCLE 



35 




Fig. 5. — Rankine Cycle for Dry Vapor 



36 VAPORS FOR HEAT ENGINES 

from which x T may be obtained when l t is tabular, and 

V s =Vr = X T V h 

very nearly, V t being also tabular. 

Such a comparison would be of little value. Expansion 
is in practice limited, not by an assigned temperature t r , 
but by a "ratio of expansion," V r +V c , which in simple 
engines has been established at about the value 4:1, as 
a compromise between technical cyclic efficiency and the 
detrimental effect of extreme cylinder condensation at 
more complete expansions. 

This makes the problem more difficult of direct analytic 
solution, in the absence of knowledge of properties other 
than the volume and entropy of the wet vapor at the state r. 
Such a formula between temperature and volume as is given 
in Appendix II does not aid us, because it is applicable only 
to dry steam. Both dryness and temperature are unknown 
at r, if the ratio of expansion V r + V c be alone assigned. 
A carefully plotted entropy diagram, on which the lines of 
constant volume were drawn at close intervals, 1 would 
permit of an easy solution; or we might employ simultaneous 
equations in the forms 

clog^+^ = clog 6 i- 6 +,-. 

Vr = XrV t = Xr(f)t r , 

latent heats of vaporization and volumes being expressed 
as functions of temperatures and c (the specific heat of the 
liquid) being not too rapidly variable. 

The method to be adopted is that suggested by the entropy 
chart, on which lines of constant volume and constant dry- 

1 See the author's Applied Thermodynamics (D.Van Nostrand Co.), 
1910, pp. 212, 223. 



THE RANKINE CYCLE 



37 



ness may be drawn. There is no lack of such charts for 
steam, and it is needless to reproduce one here. Those for 
other vapors considered have been plotted (Figs. 10 to 13) 
for this work. The one for ether (Fig. 15) is reproduced, as 



PRE8SURE. LBS. PER.EQ. IN. 







en 


o 


c 




o 


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0.1 


0.2 


A 


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DRYM 


07 

ESS | 


o's 


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c. 


D6 


0. 


10 


0. 


15 


0. 


20 
ENTR 


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OPY 


25 





30 


0. 


35 





10 







1.0 

2.0 

3.0 

4.0 

6.ol 

o 

6.0 o 

JL 
O 

7.0 g 

8.0 

9.0 

100 

11.0 

12.0 

130 

110 



Fig. 15. — Temperature-entropy Diagram for Ether 



showing the peculiar behavior of that vapor — evaporation 
during adiabatic expansion from any initial condition, an 
evaporation which merges into superheating if expansion from 
a fairly dry initial condition be sufficiently long continued. 
Most common vapors condense with adiabatic expansion 
from an initially dry condition Carbon chloride (Fig. 13) 
appears to remain practically in the " just dry" state for even 
an extreme range of expansion. 



XI 

Efficiencies in the Rankine Cycle; Economical Condenser 
Temperature 

The cycles compared will be those with initially dry 
vapor and a ratio of expansion of about 4 to 1. The tem- 
perature limits should be, as in the Clausius cycles considered, 
302° and 68° for the special vapors and 302° and 110° for 
steam. 

For steam, then, F c = 6.28 and V r should be 6.28X4 
= 25.12. The entropy diagram gives for n c = 1.6319 and 
V r = 25.12, £, = 210°. At this temperature, n u = 0.3087, 
nvi = 1.4510. Since n b = 0.4398 and n bc = 1.1921, 

0.4398-0.3087+1.1921=^X1.4510, 
and 

Xr = 0.912. 

The steam table gives V t = 27.80, so that the actual value 
of V r is close to 0.912X27.80 = 25.4, the departure from 
the assumed value being due to inaccuracy in plotting and 
reading the entropy chart. We wil use the value F r = 25.4, 
so that the ratio of expansion will in this case be 25.4^6.28 
= 4.04, instead of 4.0, as assumed. Taking the necessary 
tabular values for substitution in Eq. (J), we have 

144 
abcrs = ^ j (69.03 X 6.28) - (1 .271 X 25.4) | 

+271.6+828.1 -177.99- (0.912X899.0) 

144 
= =^(434-32.2)+271.6+828.1- 177 .99-820 

/ to 

= 74.5+ 1099.7 - 997.99 = 176.21 B.T.U. 

38 



EFFICIENCIES IN THE RANKINE CYCLE 39 

The boat expended is, as in the Clausius cycle, 1101.66 
B.T.U., so that the efficiency is 176.21 -^ 1101.66 =0.16. 

If we should proceed in this way with the other vapors 
we should find a total lack of correspondence in the order 
of efficiencies for the Rankine cycles with that of efficiencies 
for the Clausius cycles. A rather curious fact, which we 
are now to consider, will suggest a fairer comparison than 
that proposed. 

Suppose we take the case of steam, working between 
302° and 68° F. Values of V r and x T will be as for the 
cycle already considered. Then 

144 
abcrs = -^ { (69.03 X 6.28) - (0.3386 X 25.4) | 

+271.6+828.1 -177.99- (0.912X899) 

144 
= ~(434-8.6)+101.71 = 78.9+101.71 = 180.61 B.T.U., 

77o 

eabcf= 1143.53, as for the Clausius cycle, and 

Efficiency = abcrs + eabcf= 180.61 -r- 1 143.53 = 0.158. 

An increase in temperature range has thus, contrary to 
expectation, decreased the efficiency of the cycle. No such 
result would be possible with the complete-expansion Clau- 
sius cycle. Too good a vacuum, with limited expansion, 
appears to be undesirable. 

Fig. 6 suggests an explanation. Let abcde represent the 
steam cycle between 302° and 68° F., gbcdf that between 
302° and 110° F. The additional work, agfe, of the former 
cycle, is gained at an expenditure for heat of mnga. Now, 
mnga = c(t g —t a ), or, very : nearly, 42 B.T.U.: while agfe = 

(P -P a ) F e =~X 25.4 (1.271 -0.3386) = 4.4 B.T.U. The 

77o 



40 



VAPORS FOR HEAT ENGINES 



ratio of , additional work obtained to additional heat con- 
sumed, when the low temperature limit is changed from 
110° to 68°, is 4.4^-42 = 0.105; which is less than the 
efficiency of the 110° cycle, so that the change must neces- 
sarily be unprofitable. 

Analytically, if t —t a be small, so that the temperature 
along the path ag may be represented by the single symbol 




mn 



Fig. 6. — Effect of Change in Back Pressure 



t (absolute temperature), and I be the corresponding value 
of the latent heat of vaporization, the area agfe is 



t 



(t-ta). 



EFFICIENCIES IN THE RANKINE CYCLE 41 

When this is small in relation to the area tnnga — c(t ff — t a ), 
or when the quotient 

tc 

has a lower value than the efficiency of the cycle under 
consideration; then we may expect to find a lowering of the 
condenser temperature undesirable, and vice versa. The 
value of x e is, of course, very nearly 

4F C 



XII 



Rankine Cycle of Maximum Efficiency 



A new problem is thus suggested: given the upper 
temperature, t Cj and the ratio of expansion Vd + V c , at 
what lower temperature should the vapor be discharged 
in order that the efficiency may be a maximum? 

Let us take the value -— as a criterion of the desirable 
tc 

discharge temperature. For steam, with 4F C =25.4., c = 1.0. 

Table IX 

DESIRABLE CONDENSER TEMPERATURE WITH STEAM 
Four Expansions, from 302° F. 



Assumed Lower 
Temperature 


I 


v x 


) • Xe 


Xel 


68 

86 

104 

107 


1053.4 
1043.4 
1033.4 
1031.7 


928 

529.5 

313.3 

288.3 


0.0274 
0.0480 
0.0811 
0.0879 


0.0548 
0.0919 
0.1480 
0.1600 



We may infer, therefore, that as the discharge tem- 
perature is reduced from 110° to 107°, the efficiency first 
increases and afterward decreases, passing a maximum at 
some temperature between these two, and being 0.16 at the 
two temperatures stated, or practically that at its maximum. 

42 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 43 

Alcohol. This vapor gives V c , Fig. 6, as 1.139, so 
that F d = 7/=7 e = 4X1.139 = 4.556. Fig. 10 gives fc=210°; 
at which, by interpolation, 7 = 4.73. This is the V t of 
Fig. 5, in which, also by interpolation, n u = 0.2073, n u t = 
0.537. Since n & = 0.325, n bc = 0.403, we have 

0.325 - 0.2073+0.403 = x T X 0.537, 
x T = 0.971, 

and the check value of V T is 0.971X4.73 = 4.60, as against 
4.556 intended. Using this in Eq. («/), with 68° as the 
discharge temperature, 



144 
abcrs = ~ { (142.0X 1 . 139) - (0.86X4.60) 

11 o 



+206.68+277.36- 121.08- (0.971X331.77) 



144, 



= ^(160.4-3.90)+484.04-443.08 = 69.98. 



The heat expended being 492.98, the efficiency is 0.142. 

The following approximation is now necessary, as in 
Table IX. 

Table X 

DESIRABLE DISCHARGE TEMPERATURE WITH ALCOHOL 

Four Expansions, from 302° F. 



Assumed Lower 
Temperature 


I 


v x 


Xe 


X e l 

tc 


86 

122 
140 


432.92 
420.82 
409.73 


91.82 
34.20 
21.69 


0.0501 
0.1342 
0.2120 


0.065 
0.135 
0.201 



44 



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0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 

ENTROPY 

Fig. 10. — Temperature-entropy Chart for Alcohol 



0.90 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 45 

For this last lower temperature of 140°, we have 

144 

abcrs = ---{(U2.0X 1.139) -(0.78X4.60) | +484.04-443.08 

I to 

= ~(160.4 -30.8) +40.96 = 64.91; 

77o 

while the difference between the heats of the liquid at 140° 
and 08° being 67.27-20.50 = 46.71, the heat expended is 
492.98-46.71=446.27, and the efficiency is 64.91-^-446.27 
= 0.145. Again, the presumption is that maximum efficiency 
occurs at some discharge temperature between the two con- 
sidered, viz., 140° and 68°. To shorten the matter, let us 

note that 

144 
abcrs = ^(160.4 - 4.60P a ) +40.96. 

For t a = 122°, 104°, 86°, respectively, P a = 4.25, 2.59, 1.52, 
and abcrs = 67.06, 68.56, 69.36. Also for h a = 54.38, 42.68, 
31.48, as compared with 20.56 for a 68° discharge temperature, 
the reductions in heat expenditure are 33.82, 22.12, 10.92, 
and the respective heat expenditures are 459.16, 470.86, 
482.06, giving efficiencies of 0.146, 0.145, 0.144. The 
discharge temperature had better be 122° than 140°; a 
lower temperature than 122° is undesirable. Maximum 
efficiency will be attained when it is between 122° and 140,° 
probably nearer the former than the latter, and this max- 
imum efficiency will be not far from 0.146. 

Chloroform. We have, in Fig. 5, V c = 0.457, V r = 4 X 0.457 
= 1.828 (desired value). From the chart, Fig. 11, U = 181° F. 
Applying the principle 

n b — n u +n b c = x r nut J 

0.1077-0.0647+0.1219 = 0.1651 x T , 

x r = 0.998. 



46 



VAPORS FOll HEAT ENGINES 



320 T£73 T ll it 


<uo - Jt'l4 -t tv t^ 


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0^ id Jciii' ^.:v 


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970 4 QllL^tjit t'-Y 


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230 £h £4tC^I&4 


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200 £h ±^-H7^aZi^-4- 


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a 180 zii: , trtA'± 4> * 


X 170 4-4 1 Li I 4J&4 h 


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£160 lit 1 X 7 4 


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£ 150 ^ t t t/ A 


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100 ^ £ t - 4- I 


qn -4 -i L I ._.._[- I 


90 7 J , k ._ 4. 1 


80 £ 2 4 -I - --4- 4 


80 t t t i - --4- j 


70 -j J f j _ ..4- 


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tJn t - -in 


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T [ i r i r i 



0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 
ENTROPY 

Fig. 11. — Temperature-entropy Chart for Chloroform 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 47 

From the table, F* = 1.85, whence V r (value employed) 
checks as 0.998X1.85 = 1.85. By Eq. (J), with a discharge 
temperature of 104°, 



144 

abcrs = ~~{ (141. 4X0.457) -(7.14 XI. 85) 

/ to 



+64.78+81.23 -35.24- (0.998X95.42) 



144 



= ~(64.4- 13.2) + 15.67 = 25.17. 

The heat expended is 140.85, and the efficiency is 25.17 -r- 
140.85 = 0.179. 

Table XI 

DESIRABLE DISCHARGE TEMPERATURE WITH 
CHLOROFORM 

Four Expansions, from 302° F 



Assumed Lower 
Temperature. 


I 


v x 


x e 


Xgt 

tc 


86 

104 


115.38 
113.63 


10.275 
7.1 


0.1798 
0.261 


0.158 
0.218 



The best condenser temperature is between 86° and 104° 
and somewhat exceeds 0.179. 



For acetone, tabular values above 284° F., are extrapolated 
merely, and the results to be obtained must be regarded 
with some reserve. The initial volume is about 0.706; 
that at the end of expansion must then be approximately 
0.706X4 = 2.824; at which, from the chart (Fig. 12), the 



48 



VAPORS FOR HEAT ENGINES 





















































































































300 












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T. 






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0.2 



0.3 0.4 

ENTROPY 



0.5 



0.6 



Fig. 12. — Temperature-entropy Chart for Acetone 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 49 

temperature is 191° and the dryness, 0.975. Then, referring 
to Fig. 5, 

n b — riu + n bc = n ur = x r n ut , 

0.2465-0.1537+0.236 = 0.334a; r 

x r = 0.985 (accepted value), 

and since V t is 2.99, V r = 0.985X2.99 = 2.94, which value 
will be employed. For ^ = 104°, Fig. 5, Eq. (J) gives 

144 

a6crs = ^|{(164X0.706)- (8.12X2.94)! 

+ 152.78+156.02-86.09- (0.985X196.14) 
= ^|(115.7-23.7)+29.21 = 17+29.21 =46.21. 

The heat expended is h b +l bc -h a = 152.78 + 178. 13 -37.60 
= 293.31, and the approximate efficiency 46.21 -=-293.31 
= 0.158. 

Now at 104°, £ = 240.19, c = 0.534, F*(Fig. 6) = 13.13, 
x e = 2.94 -13. 13 = 0.224, and 

x e l_ 0.224 X 240.19 

tc 564X0.534 ' 

so that a somewhat lower discharge temperature is desirable. 
If this bo 86°, 

144 

a&crs = ^jll5.7- (5.42X2.94) {+29.21 =47.61, 

the heat expended is 152.78+178.13-27.99 = 302.92, and 
the efficiency is in the neighborhood of 47.61^302.92 
= 0.157. The inconsistency here is probably due to errors 
in extrapolated values, so that acetone will be ignored in 
further comparisons. 



50 VAPORS FOR HEAT ENGINES 

Carbon Chloride. Here V c = 0.510, F r = 2.04 and Fig. 13 
gives ^ = 193° with x r close to (perhaps slightly above) 
unity; values which confirm that assumed for V r . Eq. (J) 
now gives, if t a = 122°, 

144 

abcrs = ^{ (88X0.510) -(6.08X2.04)} 

+ 57.11+60.78-33.18-73.40 

144 
= ~(44.8-12.34) + 11.31 = 17.31; 

and since ea&c/=57.11+69.02- 18.22 = 107.91, the efficiency 
is 17.31-^107.91=0.16. 

At * a = 122°, 1 = 87.76, 7 = 6.554, c = 0.21, x e (Fig. 6) 
= 2.04^-6.554 = 0.31; and the efficiency criterion becomes 

x e l 0.31X87.76 



tc 582X0.21 



= 0.224. 



This justifies an investigation for 2 a = 104°, at which p a 

= 4.155 and 

144 
a6crs = ^-|(44.8-8.41) + 11.31 = 18.01, 

77o 

which with eabcf= 126.13 — 14.51 = 111.62 gives an efficiency 
of 18.01-^111.62 = 0.162. Here we have 

x e l_ (2.04^9.302)89.1 3 

tc ' 564X0.205 ' 

indicating that a still better efficiency will accompany some 
reduction in discharge temperature. If this be made 86°, 
however, p a = 2.754 and 

144 
a6crs = ^(44.8-5.66) + 11.31 = 18.58; 

<7o 

eabcf = 126.13 - 10.84 = 115.29; and the efficiency is 
18.58^-115.29 = 0.161. 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 51 





T [ 






7 


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170 I'M- 


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130 LIZI7 „ 


/ / /* / 10 20 30 4i 50 61) 7D 80 90 


10 ^jtEin? 


' .• \ CONSTANT DRYNESS, PER CENT. 


120 1 'I'lfTij' 


,7/-— f 




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no I j ti: 




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IfVI / CARBON GHlJofl 


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100 g4 f 


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qn I L 


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£4 H 


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80 -J- ti 


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t-i i 1 


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ti ti - 


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fi oXt-j ti - 


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60 1 L2J~t - 


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50 4 1-Ct - 




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40 1 ti t^ 


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30 -4o-20-30-4(H5(- 


ti i / 




CONSTANJ DRYNf 


5S, pER CENT.' 



0.05 0.10 0.15 0.20 0.05 0.10 0.15 
ENTROPY 



0.20 



0.25 0.S 



Fig. 13. — Temperature-entropy Charts for Carbon Chloride and 
Carbon Bisulphide 



52 



VAPORS FOR HEAT ENGINES 



The best discharge temperature is then between 86° and 
104°, and the corresponding efficiency is not far from 0.162. 

Finally, for carbon bisulphide, V c (Fig. 5) =0.502, 
Fr = 2.008, and Fig. 13 gives ^ = 173°, x r = 0.90. From 
the table, 7^ = 2.226, whence V r (actual value used) =2.226 % 
X 0.90 = 2.003. If we take t a at 68°, 

144 

abcrs = ^- 7 - i (176X0.502)- (5.76X2.003) | 



+66.82+101.9-34.07- (0.90X128.44) 



144 



= =^(88.3-1 1.56) + 19.05 = 33.25. 



Here ea6c/= 66.82+ 117.90 -8.53 = 176.19, and the efficiency 
is 33.25 -^ 176.19 = 0.189. Applying the criterion, 



x e l (2.003 -J- 12.879) X 158.44 



tc 



528X0.2385 



= 0.196, 



so that in this case maximum efficiency (which will not 
much exceed 0.189) will be obtained at a discharge tem- 
perature possibly a little below 68° F. 
We now tabulate these results : 



Table XII 

MAXIMUM EFFICIENCIES WITH FOUR EXPANSIONS 

Initially Dry Vapors, from 302° F. 



Vapor 



Discharge . 
Temperature 



Efficiency 



Vacuum (Inches of 
Mercury) 



Order of 
Efficiencies 



Alcohol 

Chloroform 

Carbon bisulphide 
Carbon chloride. . 
Steam 



122°-140° 
86°-104° 

below 68° 
86°-104° 

107°-110° 



0.146 
0.179 + 
0.189 + 
0.162 
0.16 



16.13 to 21.26 
15.38 to 20.17 
at 68°, 18.19 
21.46 to 24.32 
27.33 to 27.55 



RANKINE CYCLE OF MAXIMUM EFFICIENCY 53 











































'900 














































































800 
















































\ 






























700 










\ 






































\ 






























600 












\ 




































\ 


\ 


„ 


-- 






CY 


CLE 


s ri 


ITI- 


\ SUPE 


}HE 


AT 




500 










A 




\ 








































s 




\ 






c 














■100 




















\ 




























| 


J- 






























"25 




INI 


TIA 


LLY 


DRY C 


LAUSIL 


8 


























CYCLES 302- 


68" 


F. 






\ 


















24 
























s 


/ 


/ 


































s 


/ 














23 














































































22 














































































21 














































































20 














































































19 


















































/ 


\ 


RA 


NKI 


>JE 


3YC 


LEJ 


FR 


OM 


302 J 








18 












/ 


\ 


4 EXP 


ANIONS -MA> 


IMUM 


;ff 


CIE 


NC 


1 












/ 


\ 






1 


V 


















17 










/ 




\ 






/ 


\ 


























/ 




\ 


1 




/ 




\ 
















16 










/ 










r^ 




\ 






























\ 


/ 






















15 
















\ 


/ 






































/ 































































OI 
mo. 
a. -i 



Fig. 14. — Cyclic Efficiencies and Criterion 



54 VAPORS FOR HEAT ENGINES 

The order of efficiencies is strikingly different from that 
for those cycles in which expansion is complete. It is note- 
worthy also that with some of the vapors the best efficiency 
is attained with only a moderate degree of vacuum. Alcohol 
is the only vapor showing a lower efficiency than steam; 
those with the other vapors are such as to justify the expecta- 
tion of saving from 1 to 18 per cent of the fuel by their 
substitution for steam. 

In compound condensing engines, with ratios of expan- 
sion greatly exceeding 4, the most economical discharge 
temperature would probably be the lowest attainable, 
and the efficiencies of the various vapors would rank more 
nearly in the order found for the Clausius cycle. 

T—t 
The use of the — =— criterion furnished by the Carnot 

cycle is wholly unreliable; but it is a curious fact that in 
Table XII the efficiencies rank very nearly in the order of 
the temperature ranges. 

Some graphical expressions for both the Clausius and 
Rankine cycle results are given in Fig. 14. 



XIII 

Commercial Factors with the Rankine Cycle 

If we apply the principles already enunciated for the 
cycles of complete expansion, we have, in Fig. 5, 



— — = efficiency, as an inverse measure of the relative boiler 
eabcf 

capacities necessary; 



abcrs 

~~hl x v °l ume °f liquid, as an inverse measure of the relative 

" times to get up steam"; 

easrf eabcf— abcrs „ ^ , ,. „ 

-= — - = — — —i , as a measure of the relative amounts of 

abcrs abcrs 

condenser surface and cooling water necessary; 
and (a new feature) 

V =V S 

-~ -, as a measure of the relative sizes of cylinder necessary 

for a given output. 



The comparisons are shown graphically in Fig. 7. Alcohol 
is an unattractive vapor on account of its low efficiency. 
Carbon bisulphide presents the unusually desirable features 

55 



R HEAT ENGINES 



100 




99 




85 




StoH 




110 



Steam 



100 



Carbon 
Chloride 



Carbon 
bisulphide 



Chloroform 
Relative Boiler Capacities Necessary 




Steam Carbon 

Chloride 



Carbon Chloroform 

Bisulphide 



Alcohol 



84^ 



Alcohol 
Relative Times to "Get Up Steam" in the Same Boiler 



100 




99 




82 




87 




112 



Steam 



Carbon 



Carbon 



Chloroform 



Alcohol 



Chloride Bisulphide 

Relative Amounts of Condenser Surface and Cooling Water 



100 










78 
















42 




51 




41H 



Steam 



Carbon Carbon Chloroform 

Chloride Bisulphide 

Relative Sizes of Cylinders 



Alcohol 



Fig. 7. — Comparative Proportions of Power Plants Using Various 
Fluids in the Rankine Cycle from 302° F., with Four Expansions. 
All Developing the Same Horse-power 



RANKINE CYCLE— COMMERCIAL FACTORS ;>< 

of highest efficiency, maximum cylinder capacity, minimum 
condenser surface and cooling water consumption, min- 
imum boiler capacity; and a " time to get up " pressure 
only 5 per cent greater than is necessary with steam. 

Table XIII 

BOILER CAPACITY AND STEAMING RATE 

Rankine Cycles, Four Expansions, Dry Vapor from 302° F. 



Vapor 



Efficiency 



Relative 

Boiler 
Capacity 
Necessary 



Volume 

of 
Liquid 



Volume 

X 

Efficiency 



Relative 
Time to 
"Get Up 
Steam " 



Alcohol 

Chloroform 

Carbon bisulphide 
Carbon chloride. . 
Steam 



0.146 
0.179 
0.189 
0.162 
0.16 



110 

89£ 
85 
99 
100 



0.0208 
0.0096 
0.0130 
0.0069 
0.0160 



0.00304 
0.00172 
0.00245 
0.00112 
0.00256 



150 
105 
229 
100 



Table XIV 

CONDENSER SURFACE AND COOLING WATER 
CONSUMPTION 

Rankine Cycles, Four Expansions, Dry Vapor from 302° F. 



Vapor 


abcrs 


eabcf 


easrf 


easrf -5- 
abcrs 


Relative Conden- 
ser Surface and 
Cooling Water 
Consumption 


Alcohol 


67.06 
25.17 
33.25 
18.01 
176.21 


459.16 
140.85 
176.19 
111.62 
1101.66 


392.10 
115.68 
142.94 
93.61 
925.45 


5.85 
4.58 
4.30 
5.20 
5.25 


112 


Chloroform 

Carbon bisulphide 
Carbon chloride. . 
Steam 


87 

82 

99 

100 





58 



VAPORS FOR HEAT ENGINES 



Table XV 

SIZE OF CYLINDER FOR A GIVEN OUTPUT 

Rankine Cycles, Four Expansions, Dry Vapor from 302° F. 











Relative 


Vapor 


abcrs 


V 


V r + abcrs 


Volume of 
Cylinder 


Alcohol 


67.06 


4.60 


0.0685 


47± 


Chloroform 


25.17 


1.85 


0.0735 


51 


Carbon bisulphide .... 


33.25 


2.003 


0.0602 


42 


Carbon chloride 


18.01 


2.04 


0.1125 


78 


Steam 


176.21 


25.4 


0.1440 


100 







XIV 



Rankine Cycles with Superheat 

Not enough is known of the properties of these vapors 
when in the superheated condition to warrant the attempt 
to solve comparative cycles of this type. Even for steam, 



5 
a 

I" 

Ih 




d 


9\^ 


e 


J A 




7 


J x 


\ 

n 



5 


e 


S \ 
\ \ 


9^' 






f 





m 3 



N 



Fig. 8. — The Rankine Cycle with Superheat 



the last word has probably not been said on such properties. 
The following method for computing the efficiency etc., 
of any Rankine cycle with the vapor initially superheated, 
is believed to be accurate and perfectly simple: requiring 
only exact values for the specific heats and entropies calcu- 
lated therefrom. The need of the method arises from the 

59 



60 



VAPORS FOR HEAT ENGINES 



inaccuracy in computing the work along an even partially 



superheated adiabatic, either by the 



pv- 



PV 



1 



formula or 



by an expression for the loss of internal energy The present 
method may be considerably shortened by the employment 
of the Mollier or total-heat entropy diagram 

Case I Let expansion be wholly in the superheated 
region, the steam becoming saturated (dry or wet) during 
the terminal drop - cycle abcdef, Fig. 8. Then 



Efficiency 



Work 



abcdef 



Heat expended mabcdri 
Draw the line of constant pressure egh through e. Then 
hbcdeg-\-ahgef 



Efficiency 



mabcdn 



144 



(jhbcdn-jhgen) + - f7 - { (P h V e ) - (P a V e ) 
mabcdn 

H d -h h -H e +h h +~(P h -P a )V e 
H d —h a 

H i -H e +~V e {P h -P a ) 



Hd~h a 



H d and H e being the total heats above 32° F., at the states 
denoted by their subscripts, h a the heat of the liquid at a, 
and V and P pressures and volumes. The entropy and 
volume at e determine the total heat and pressure at that 
point. 



RANKINE CYCLES WITH SUPERHEAT 61 

Case II. If the vapor remains superheated at the end 
of the terminal drop (i.e., at the point /), the computation 
is unaltered, and the fact of such superheat might even 
be unsuspected. 

Case III. If the vapor becomes saturated during 
expansion, its initial entropy must have been less than that 
of the dry vapor at the terminal pressure. This is the most 
probable case, and the condition is sure to be detected when 
the total heat is ascertained at e. The saturated steam 
tables will give H e , and the expression for efficiency is not 
changed. * 



XV 

Summary: Conclusions 

The use of a special vapor to replace steam might be 
justified on one of three grounds: 

(a) A reduced lower temperature limit for the cycle without 
the necessity for an impracticably high vacuum. The extreme 
limit is determined, however, by the cooling water supply, 
and the gain in this direction appears likely, from a rigid 
application of the second law of thermodynamics, to be 
small. 

(b) But the properties of the substitute vapor may be such 
as to cause a greater gain than is thus indicated. Examination 
shows that steam ranks best as to the critical ratio 

Latent heat of vaporization 
Specific heat of liquid ' 

between certain assumed temperature limits, at which, 
correspondingly, it gives the highest efficiency. These limits 
(302° and 68° F.) are impracticable for steam, though 
practicable with the other vapors. With a more practicable 
lower limit of 110° F. for steam, it gives with complete 
expansion an efficiency below that attainable by the other 
(saturated) vapors. This comparison is of practical impor- 
tance only with the turbine engine. The velocities attained \ 
by complete adiabatic expansion between the assumed » 

62 



1 



SUMMARY: CONCLUSIONS 63 

limits arc with the substitute vapors in all cases much less 
than those attained with steam. 

In cycles with terminal drop, at such ratios of expansion 
as are common in simple engines, all of the vapors except 
alcohol surpass steam in efficiency, but this superiority is 
not traceable to a reduced lower temperature limit. This 
limit is sometimes too low for best efficiency in the simple 
condensing engine. The limit at which the efficiency is a 
maximum may be approximated from the variation in the 
determining ratio 

xj> 
tc' 

Maximum efficiencies for the various saturated vapors 
in this type of cycle occur at lower temperature limits rang- 
ing all the way from 68° to 140° F. 

The total unreliability of any surmises based on the 
Carnot expression, 

T-t 



is evident. It may be objected that the use of a uniform 
expansion ratio of 4 : 1 in all cases is an improper assumption : 
that in a vapor showing relatively slight — or no — condensa- 
tion with adiabatic expansion, the influence of cylinder con- 
densation would be so mitigated that the ratio of expansion 
might be advantageously increased. But cylinder condensa- 
tion means virtually heat transfer; and this heat transfer 
would go on just the same as long as the substance re- 
mained a wet vapor. Further, the evils of such transfer are 
largely evidenced in initial condensation; that which occurs, 
not during expansion, but during admission of steam to the 
cylinder. A given loss of heat to the walls actually means a 
greater loss of dryness in the case of the substitute vapors, 



64 VAPORS FOR HEAT ENGINES 

because the heat contents of given weights of such vapors 
are less than those of the same weight of steam. This may 
appear an argument in favor of the use of a lower ratio of ex- 
pansion in their case : but, on the other hand, the substitute 
vapors uniformly contain more heat and give more work, 
in proportion to the space which they occupy. 

(c) The capacity of the apparatus may be affected by 
the properties of the fluid chosen. It appears that there are 
perceptible advantages with some of the substitute vapors 
in respect to boiler capacity, time of getting into operation, 
condenser capacity and amount of cooling water necessary, 
as long as we limit the consideration to the complete expan- 
sion type of cycle. With the terminal drop cycle, the vapors 
maintain their advantage in all respects excepting that of 
" quick steaming" : and they produce from 50 to 75 per cent 
more power from a cylinder of given size than does steam. 

The objections to the use of a substitute fluid include: 

(a) Its cost. This need not be prohibitive, if the leakage 
loss is not excessive in proportion to the gain of efficiency. 

(b) Increased maximum pressure. This is associated 
with all of the fluids, with the possible exception of carbon 
chloride at high temperatures. This substance comes 
nearest to the desired pressure-temperature relation, 
standing to steam in much the same relation as it does 
to alcohol at a lower temperature. Its pressure-temperature 
curve is of abnormally slight slope. 

The binary vapor principle permits of a slight gain 
without excessive maximum pressure; but involves more 
complication than would the use of a substitute vapor. 
In practice, pressure conditions influence the cyclic range 
and superheating may be resorted to in order to increase 
the range. With superheat, a high specific heat of the 
superheated vapor and a left-hand location for the pressure- 
temperature curve (Fig. 2) furnish criteria of desirability. 



SUMMARY: CONCLUSIONS 65 

The disadvantage of an increased maximum pressure 
may be offset by the reduction in size of cylinder probable 
with all of the substitute fluids. The only remaining 
question is, then, whether with such a fluid a sufficient 
increase in efficiency may be obtained to offset the expense 
due to leakage. With superheat and complete expansion 
the answer appears to be in the negative. With only 
saturated vapor employed, we have found at least one con- 
dition at which, with carbon bisulphide, for example, leakage 
amounting to the percentage 

18 

or 

might be tolerated, a representing the ratio of the cost of 
carbon bisulphide, pound for pound, to that of coal. 

The properties of some of the vapors are not known 
with great exactness, and the figures presented are in all 
cases approximate. Investigation of terminal drop cycles 
with, say, 16 expansions, both saturated and superheated, 
is warranted; but on the whole it seems safe to say that 
there is nothing inherently absurd in the proposal to use 
some vapor other than steam for power production. The 
substitution appears far more promising than the use of a 
binary vapor on the steam cylinder exhaust. 



APPENDICES 



APPENDIX I 
The Vapors Discussed 

The alcohol referred to (C2H6O), is the ordinary ethyl 
alcohol (not wood alcohol); a light colorless, inflammable, 
rather pleasant-smelling liquid. When free from water its 
specific gravity is 0.785. It boils at 172° F., and has been 
frequently used as a working fluid in heat engines. 

Chloroform (C2HO3), known from its use as an anaesthetic, 
is a heavy clear fluid of powerful odor, specific gravity about 
1.48, boiling-point 140-144° F. The commercial product 
sells for about 25 cents a pound. 

Acetone (C3H6O), is a colorless liquid of specific gravity 
0.797 and boiling-point 135° F. 

Carbon Bisulphide (CS2), costs (in a somewhat impure 
state) about 4 cents a pound. It is a poisonous pungent- 
smelling clear liquid, boiling at 115° F. The specific gravity 
is 1.27. 

Carbon Chloride (CCU, the tetrachloride), boils at 168- 
171° F., is 1.6 times as heavy as water, and costs about 8 
cents a pound. It has recently been employed as a cleansing 
fluid in place of gasoline. It is claimed that it can be 
manufactured on a large scale at a cost much below the 

67 



VAPORS FOR HEAT ENGINES 



present price. The ordinary commercial substance is a 
transparent fluid, with an odor suggesting garlic. It is 
slowly hydrolized by water, forming CO2 and HC1. 

These fluids, with ether, gasoline and 90 per cent benzol, 
are all grease solvents; most of them are inflammable, but 
in this respect chloroform and carbon chloride are exceptions. 
All seem to be non-corrosive in their action on iron pipes or 
plates. Reference should be made to the paper by Booth, 
" Commercial Extraction of Greases and Oils," Trans. Am. 
Inst. Chem. Engrs., II, 1909, 248: and to p. 114 of Gill's 
" Oil Analysis," relating to the action of oils on metals. 



APPENDIX II 

The Volume Temperature Relation of Dry Steam 

The sources from which a relation between the volume and 
temperature of saturated steam must be found are, essentially, 
the exponential equations of Rankine and Zeuner for the 
pressure-volume relation, 

PV n = constant, 

where P and V are corresponding specific pressures and 
volumes and n is either -}-J (Rankine) or 1.0646 (Zeuner): 
and the Thiesen formula for pressure-temperature, 

Hog y|y = 5.409(7 7 -212) -8.71 Xl0- 10 [(689-7 7 ) 4 -477 4 ], 

in which t is the absolute and T the Fahrenheit temperature, 
and P is in pounds per square inch. The pressure-volume 
formula is an empirical expression intended to describe 
the results following the application of the well-known 
Clapeyron differential equation from which specific volumes 
are usually calculated. The pressure-temperature expres- 
sion is also empirical, but stands on a somewhat more satis- 
factory footing, expressing the results of recent experimental 
work so closely that it has been used in computing the 
lately published steam tables of Marks and Davis. It is, 
however, too cumbersome for our purpose, which is that 

69 



70 



VAPORS FOR HEAT ENGINES 



of deriving a fairly accurate and quickly available expres- 
sion for the relation between volume and temperature. 

We will adopt the Marks and Davis tables (Longmans, 
Green & Co., 1909) for reference. A recent magazine 
article (Power, March 8, 1910), gives the surprisingly accurate 
expression, 

*=200p*-101, 

for pressure (pounds per square inch) and temperature 
Fahrenheit. This gives confirmation of tabular values with 
an error not exceeding that involved in computation with a 
10-inch slide rule. If we combine this equation with that 
between pressure and volume, we find 

P* = ^^ = 0.005^+0.505, 
pt;H=(0.005*+0.505) 6 t;H = a constant, 477, 
the approximate evaluation of which is as follows: 



t 


o 

lO 

£+ 

>o 

o 
o 

© 


log (7) 


6 log (7) 


76 


All 


log »I5 


s 

O 

bio 
M 


V 


101.83 1.01415 


0.00610.0366 


1.089 437.5 


2.6418 


2.49 


309 


153.01 


1.270 


0.104 


0.624 


4.2 


113.5 


2.056 


1.934 


85.9 


182.86 


1.419 


0.152 


0.912 


8.16 


58.4 


1.766 


1.661 


45.8 


200 


1.505 


0.178 


1.068 


11.69 


40.9 


1.612 


1.516 


32.8 


220 


1.605 


0.206 


1.236 


17.2 


27.9 


1.446 


1.359 


22.82 


240 


1.705 


0.232 


1.392 


24.62 


19.36 


1.2877 


1.211 


16.23 


260 


1.805 


0.2565 


1 . 5390 


34.58 


13.8 


1 . 1402 


1.072 


11.8 


280 


1.905 


0.28 


1.68 


47.9 


9.97 


0.998 


0.938 


8.66 


300 


2.005 


0.3023 


1.8138 


65.04 


7.315 


0.864 


0.812 


6.49 


320 


2.105 


0.324 


1.944 


87.9 


5.43 


0.735 


0.691 


4.91 


340 


2.205 


0.344 


2.064 


115.8 


4.125 


0.616 


0.58 


3.8 


401.1 


2.5105 


0.4 


2.4 


251 


1.9 


0.28 


0.264 1.835 



APPENDICES 



71 



40 60 



Pressure. LbB. per Sq. In. 
100 120 140 160 180 200 220 240 



16.0 




Entropy above 32 °F„ B.t.u; 

Fig. 16. — Temperature-entropy Diagram for Ammonia 



72 



VAPORS FOR HEAT ENGINES 



The values of v closely correspond with those in the 
steam table adopted, excepting in the case of the lower 
temperatures — below 200°. A simpler formula is, however, 
desirable. 

If we assume the possibility of an expression in the form 
tv n = constant, then by successive trials we may find the 
most plausible value of n to be 0.248, and 

fe°- 248 = 477|. 

This gives the following approximate results. 



V 


log V 


0.248 log v 


^0.248 


t 


30 


1.4776 


0.3663 


2.323 


206 


25 


1.398 


0.3465 


2.22 


216 


20 


1.3016 


0.3233 


2.102 


227 


15 


1.176 


0.2919 


1.958 


244 


10 


1.0 


0.248 


1.77 


270 


8 


0.936 


0.2315 


1.701 


281 


5 


0.6985 


0.1725 


1.488 


321 



Between the tabulated limits, this has an accuracy 
within one or two degrees; but it is wholly unreliable for 
either very low or very high temperatures. Fortunately, 
it is the medium temperatures (between 200° and 260°) 
that we are principally concerned with; and within this 
range the temperature varies very nearly inversely as the 
fourth root of the specific volume — a convenient statement in 
the absence of logarithms. The fact that both expressions 
given have about the same constant term is a curious 
coincidence. 

In Fig. 9, the tabular volume-temperature curve has been 
plotted along with that given by the latter of the two equa- 



APPENDICES 



73 



tions. There would be no purpose served by plotting the 
more accurate values from the former equation, which within 
the charted limits, and to the scale adopted, actually coincide 



30 


\ 










































ores TABULAR OR 
e — 

005 t ■+ 0.505) V ,6 =477; 
OTES <V°-= 8 477 '/a 








(o- 






'** 














20 










s vv 






















10 










^^s 


^>> 


































^**> 


=**»» 









































210 220 230 240 250 260 270 280 290 300 310 320 330 340 
TEMPERATURES FAHRENHEIT 

Fig. 9. — Temperature- volume Curves of Dry Steam 



with those of the tabular curve, the departure from coin- 
cidence being less than 1 per cent even at a temperature 
above 400°. The error rapidly increases, however, as the 
temperature is lowered below 200°, being about 3 per cent 
at 183°, 5 per cent at 153° and 7 per cent at 102°. 



74 



VAPOKS FOR HEAT ENGINES 









saw 


niOA DldlD3dS 
































s 


1 


^ 2 


s 


1 


-4 




- r x 




"^ 








V 










g 

d 
















>ft> 


^ 
















l S 








CI 














*> 


















\ 


\ 








d 










§s 







<| 








cv 


v 


; 


\ 


\ 




-*"=> 












V 




>?> 


-< 


J 








/v 








*^\ 


', 








= 






£ 


7 


^ 


s>-> 


s 


H 






/y^ 


9 


\ 




\ 


1 




. 






„ 




*7 








10 


-V^Z 










\ 








^ 


■^ 


'- 




d 






57 






V" 






o/ 




\ 






**\ 




\ 


\ 


\ 






















J 






y> 






\ 




\ 


\ 


\ 






d 
















A 


/ 


V 




\ 




\ 










r= 




















/' 


' 






\ 






\ 




\ 


T 


\ 




° 


























\ 










\ 


\ 




W 


















\ 








0>\ 




\ 




\ 









d 




















r^ 




-\_ 


_^ o 


\ 




\ 




\ 


\ 


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TABLES 



75 



TABLE XVL— PROPERTIES OF THE DRY SATURATED 
VAPOR OF ALCOHOL 

Note. Tables XVI to XX are abstracted by permission from Klein's Translation 
of Zeuner's Technical Thermodynamics. (D. Van Nostrand Co.) 









Internal Latent 


Specific Volume 




Heat of the 


Latent Heat 


Heat of 


of Dry Vapor — 


Temperature, 
Fahrenheit 


Liquid above 
32°, B.T.U. 


of Vaporization, 
B.T.U. 


Vaporization, 
B.T.U. 


Specific Volume 

of Liquid, 

Cu.Ft. 


32 


0.00 


425 . 70 


402 . 18 


513.989 


50 


10.06 


429.86 


405.62 


277.595 


68 


20.56 


433.04 


407 . 90 


156.956 


86 


31.48 


432.92 


406.95 


91.800 


104 


42.68 


428.92 


402.29 


55 . 289 


122 


54.38 


420.82 


393.74 


34.174 


140 


67.27 


409.73 


382.38 


21.671 


158 


80.24 


397.12 


369 . 60 


14.112 


176 


93.80 


383.56 


355 . 94 


9.430 


194 


107.95 


370.85 


343.08 


6.479 


212 


122.72 


358.42 


330.49 


4.564 


230 


138.13 


347.15 


318.97 


3.305 


248 


154.21 


336.29 


307.85 


2.443 


266 


170.96 


325.84 


297 . 10 


1.845 


284 


188.46 


316.44 


287.31 


1.424 


302 


206.68 


306.86 


277.36 


1.118 



TABLE XVIL— SATURATED VAPOR OF CHLOROFORM 



32 


0.00 


120.60 


112.45 


37.899 


50 


4.19 


118.88 


110.36 


23.536 


68 


8.41 


117.14 


108.29 


15.314 


86 


12.64 


115.38 


106.23 


10.265 


104 


16.87 


113.63 


104.20 


7.090 


122 


21.13 


111.84 


102.15 


5.025 


140 


25.42 


110.03 


100.11 


3.646 


158 


29.72 


108.20 


98.05 


2.702 


176 


34.04 


106.36 


96.00 


2.042 


194 


38.38 


104.49 


93.92 


1.571 


212 


42.73 


102.62 


91.85 


1.230 


230 


47.11 


100.71 


89.75 


0.977 


248 


51.50 


98.80 


87.65 


0.788 


266 


55.91 


96.86 


85.52 


0.644 


284 


60.34 


94.91 


83.38 


0.533 


302 


64.78 


92.94 


81.23 


0.447 


320 


69.25 


90.95 


79.05 


0.378 



76 



VAPORS FOR HEAT ENGINES 



TABLE 


XVIII.— SATURATED VAPOR OF ACETONE 


Temperature, 
Fahrenheit 


Heat of the 


Latent Heat 


Internal Latent 
Heat of 


Specific Volume 
of Dry Vapor — 


Liquid above 
32°, B.T.U. 


of Vaporization, 
B.T.U. 


Vaporization, 
B.T.U. 


Specific Volume 

of Liquid, 

Cu.Ft. 


32 


0.00 


252.90 


237.34 


68.206 


50 


9.18 


250.22 


233 . 19 


42.851 


68 


18.52 


247.20 


228 . 96 


28.043 


86 


27.99 


243.86 


224.76 


18.932 


104 


37.60 


240.19 


220.38 


13.111 


122 


47.36 


236.19 


215.82 


9.286 


140 


57.26 


231.87 


211.06 


6.707 


158 


67.30 


227.22 


206.05 


4.937 


176 


77.49 


222.23 


200.77 


3.696 


194 


87.82 


216.92 


195.23 


2.811 


212 


98.30 


211.26 


189.38 


2.171 


230 


108.90 


205.31 


183.29 


1.700 


248 


119.66 


199.01 


176.90 


1.347 


266 


130.57 


192.39 


170.25 


1.081 


284 


141.61 


185.43 


163.29 


0.876 



TABLE XIX.— SATURATED VAPOR OF CHLORIDE OF 
CARBON 



32 


0.00 


93.60 


87.40 


52.196 


50 


3.58 


92.61 


86.16 


31.990 


68 


7.18 


91.57 


84.86 


20.465 


86 


10.84 


90.37 


83.42 


13.569 


104 


14.51 


89.13 


81.94 


9.295 


122 


18.22 


87.76 


80.34 


6.547 


140 


21.96 


86.33 


78.70 


4.729 


158 


25.74 


84.78 


76.97 


3.489 


176 


29.56 


83.12 


75.15 


2.624 


194 


33.39 


81.40 


73.29 


2.006 


212 


37.26 


79.56 


71.35 


1.554 


230 


41.17 


77.65 


69.36 


1.219 


248 


45.11 


75.62 


67.29 


0.966 


266 


49.09 


73.49 


65.15 


0.772 


284 


53.08 


71.30 


63.00 


0.622 


302 


57.11 


69.02 


60.78 


0.503 


320 


61.20 


66.60 


58.47 


0.408 



TABLES 



77 



TABLE XX —SATURATED VAPOR OF BISULPHIDE OF 
CARBON 









Internal Latent 


Specific Volume 




Heat of the 


Latent Heat 


Heat of 


of Dry Vapor — 


Temperature, 


Liquid above 


of Vaporization, 


Vaporization, 
B.T.U. 


Specific Volume 


Fahrenheit 


32°, B.T.U. 


B.T.U. 


of Liquid, 










Cu.Ft. 


32 


0.00 


162.00 


149.02 


28.172 


50 


4.25 


160.31 


146.90 


18.762 


68 


8.53 


158.44 


144.62 


12.866 


86 


12.83 


156.39 


142.20 


9.058 


104 


17.17 


154.15 


139.63 


6.526 


122 


21.53 


151.76 


136.93 


4.801 


140 


25.94 


149.16 


134.06 


3.599 


158 


30.35 


146.41 


131.07 


2.742 


176 


34.81 


143.46 


127.91 


2.123 


194 


39.29 


140.35 


124.63 


1.666 


212 


43.81 


137.05 


121.19 


1.323 


230 


48.35 


133.58 


117.62 


1.064 


248 


52.92 


129.92 


113.: «9 


0.863 


266 


57.53 


126.09 


110.03 


0.708 


284 


62.15 


122.10 


106.05 


0.586 


302 


66.82 


117.90 


101.90 


0.489 



78 



VAPORS FOR HEAT ENGINES 





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